Measuring clock and oscillator frequency

A clock may refer to an oscillator that has been designed to provide a timing signal to facilitate operation of one or more synchronous processors. In contrast, asynchronous operation does not require a clock because each step initiates upon completion of a prior step. It is potentially faster than synchronous operation because there is not the bottleneck caused by the timing device. But increased design complexities are an issue. Despite promise for the future, asynchronous operation is not widely used at present, so the clock remains a necessary component.

The fundamental oscillator in digital designs is built around an LC or RC resonant circuit, which is associated in various configurations with an amplifier driven beyond its linear range. This type of oscillator has limited frequency stability under differing amounts of loading and with power supply fluctuations. Temperature and component aging also cause frequency drift. So in most digital applications such as microprocessor clocking, the quartz crystal oscillator is used.

A precisely machined quartz crystal is substituted for the LC or RC tank circuit in various oscillator types. Since the quartz crystal is the frequency-determining component, a high degree of frequency stability is maintained regardless of temperature, component aging, and other variables.

Other crystals will work but quartz is generally used because it is sufficiently strong to resist breakage from long-term vibration. Also, quartz is easy to mill and the raw materials are readily available.

A thin quartz crystal slab, when a voltage is applied, exhibits the piezoelectric effect. It vibrates at a frequency determined by the dimensions of the quartz slab. The vibrations, in turn, create an oscillating voltage, which is extracted through terminals bonded to opposite sides of the crystal. The frequency is inversely proportional to the crystal’s thickness measured between the two precisely ground and metalized sides.

A quartz crystal is equivalent to simultaneous parallel and series resonant circuits, so associated reactive devices tune the oscillator to the output of one or the other (not both), whereupon it becomes a highly stable and reliable frequency source. The Q-factor, a measure of spectral purity, may be as high as 200,000, compared to a conventional LC oscillator with a Q-factor under 1,000.

A typical equivalent circuit for a quartz crystal.

Microprocessors generally have two oscillator pins labeled in the schematic Osc 1 and Osc 2. They are inputs from the quartz crystal oscillator, which synthesizes a continuous stream of square-wave pulses.

There are several effects to keep in mind when making measurements of crystal oscillators. Crystals have an equivalent circuit consisting of an RLC circuit in parallel with a separate capacitance (resulting from the metal case). A point to note is that measurement probes as used with oscilloscopes typically have some parallel capacitance. So positioning a scope probe across the crystal introduces some additional capacitance.

This additional capacitance can be problematic. In some cases, it can be enough to pull the oscillation frequency of the crystal by a few hundred parts per million. (As a quick review, oscillators and other frequency control devices specify their frequency variation in units of parts per million (ppm). The relationship is Δf = (f×PPM)/106. Here PPM is the peak variation (expressed as ±), f is the center frequency (in Hz), and Δf is the peak frequency variation (in Hz). For example, 100 ppm of 100 MHz represents a variation in frequency (Δf) of 10 kHz. The maximum and minimum frequencies are therefore 100.01 and 99.99 MHz, respectively.)

Crystal supplier ECS Inc. provides this data to show how the oscillating frequency of its crystals typically change with capacitive loading.

In simple crystal oscillator circuits, capacitive loading from a scope probe might even be enough to prevent the crystal from oscillating. One way to minimize such difficulties is to use a low-capacitance scope probe. For example, Tektronix makes a probe called the TPP1000 that is designed to be used with its MDO3000 scope which exhibits just 3.9 pF of capacitive loading. There are similar probes available for other Tek scopes.

Modern high-performance digital can run measurements on signal cycles that are acquired within a single capture. Unfortunately, memory limitations often force them to capture only a small time slice of a signal (typically up to 1 msec) at their maximum sampling rate. This effectively limits the measurement accuracy. The primary objective for an oscilloscope time base is low jitter, so scopes don’t have good frequency stability. The situation can be corrected by using a stable external reference such as a rubidium time base, stable to 1 ppb (parts per billion), or better yet, a GPS-disciplined time source good to 0.1 ppb.

Another point to note is that oscilloscopes take frequency measurements for every period of the input signal. Depending on the scope settings, the instrument may average results over multiple captures or over all signal periods within a single capture. The problem is that a frequency measurement on a single sampling period can be affected by signal period jitter and the scope’s internal noise, causing the results to change by thousands of parts per million. Collecting thousands of samples and taking the average significantly reduces the error. But in situations demanding a super-precise frequency measurement, the preferred means of getting ppm-level accuracy is to use a frequency counter.

Modern frequency counters use a technique called reciprocal counting to make a frequency count. With this method, the gate (measurement) time is synchronous with the input signal, so the measurement error is limited to one reference clock cycle. For better resolution, the reference frequency is multiplied. The main advantage of this approach is that resolution is independent of input frequency.

A typical connection for making frequency counter measurements.

There are additional methods that further boost measurement resolution by time-stamping start and stop input signal edges. This makes it possible to determine when those events happen within the reference clock cycle. Modern frequency counters can hit 20-psec resolutions or better.

Because loading of the oscillator circuit can affect frequency measurements, some thought must go into the connection of the signal-under-test to a frequency counter. A common practice it to use 50-Ω coax, assuming the instrument input is 50 Ω, coupled to the test circuit through a resistor (often 1 kΩ) meant to isolate the DUT from the external load. This probing scheme (with 1 kΩ resistance) has a 21:1 attenuation factor.